The classical pathway of complement is initiated by the C1 complex, a multimolecular protease comprising a recognition subunit (C1q) and two modular serine proteases (C1r and C1s) associated as a Ca2+-dependent tetramer (C1s-C1r-C1r-C1s). Early studies have allowed identification of specialized functional domains in these proteins and have led to low-resolution models of the C1 complex. The objective of current studies is to gain deeper insights into the structure of C1, and the strategy used for this purpose mainly consists of dissecting the C1 components into modular fragments, in order to solve their three-dimensional structure and establish the structural correlates of their function. The aim of this article is to provide an overview of the structural and functional information generated by this approach, with particular emphasis on the domains involved in the assembly, the recognition function, and the highly specific proteolytic properties of C1.